There's a more subtle reason that issuing credit cards is useful for banks.
One of the most basic ways that banks make money is by taking the money that one person has deposited, using that to issue loans to others, and then charging interest on those loans. With me so far?
Ok, so when you have a credit card, that simply transfers money from one account to another, meaning that the money you originally deposited with the bank remains in the bank's control for longer.
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Example 1 - without a credit card:
You deposit £1,000 in the bank.
Later, you decide to buy something worth £1,000. You withdraw the money from the bank and use it to settle the bill. The bank no longer has that £1,000 deposit to use to support loans to others.
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Example 2 - with a credit card:
You deposit £1,000 in the bank. You also have a credit card for convenience and because like Valis you are trying to build your credit rating.
You decide to buy something worth £1,000. This time, you pay for it with your credit card.
In this example, the bank still has your £1,000 deposit and can use it for lending purposes.
Does that make sense?